A person who has been specially trained and conditioned for excellence in

Mentats are described as a "class of Imperial citizens trained for supreme accomplishments in logic."

"Your mother wanted me to be the one to tell you, Son. You see, you may have Mentat capabilities."
Paul stared at his father, unable to speak for a moment, then: "A Mentat? Me? But I . . . "
"Hawat agrees, Son. It's true."
"But I thought Mentat training had to start during infancy and the subject couldn't be told because it might inhibit the early . . . " He broke off, all his past circumstances coming to focus in one flashing computation. "I see," he said.
"A day comes," the Duke said, "when the potential Mentat must learn what's being done. It may no longer be done to him. The Mentat has to share in the choice of whether to continue or abandon the training. Some can continue; some are incapable of it. Only the potential Mentat can tell this for sure about himself."
Paul rubbed his chin. All the special training from Hawat and his mother -- the mnemonics, the focusing of awareness, the muscle control and sharpening of sensitivities, the study of languages and nuances of voices -- all of it clicked into a new kind of understanding in his mind.
"You'll be the Duke someday, Son," his father said. "A Mentat Duke would be formidable indeed. Can you decide now . . . or do you need more time?"
There was no hesitation in his answer. "I'll go on with the training."

Here's how the Baron Harkonnen describes the twisted Mentat-Assassin Pitr de Vries:

"This is a Mentat, Feyd. It has been trained and conditioned to perform certain duties. The fact that it's encased in a human body, however, must not be overlooked. A serious drawback, that. I sometimes think the ancients with their thinking machines had the right idea."

"They were toys compared to me," Piter snarled. "You yourself, Baron, could outperform those machines..."
"I give you an order, Mentat. Perform one of your various functions."
"So be it," Piter said. He straightened, assuming an odd attitude of dignity -- as though it were another mask, but this time clothing his entire body.

Thufir Hawat, the Duke Atreides Master of Assassins, also enters altered states when speaking as a Mentat - it is referred to as a "Mentat semitrance." It's also described as "intense Mentat concentration."

First Law of Mentat...: 'A process cannot be understood by stopping it. Understanding must move with the flow of the process, must join it and flow with it.'

The Lady Jessica, an adept of the Bene Gesserit, describes Mentats this way, speaking to Thufir Hawatt:

The natural human's an animal without logic. Your projections of logic onto all affairs is unnatural, but suffered to continue for its usefulness. You're the embodiment of logic--a Mentat. Yet, your problem solutions are concepts that, in a very real sense, are projected outside yourself, there to be studied and rolled around, examined from all sides."
"You think now to teach me my trade?" he asked, and he did not try to hide the disdain in his voice.
"The finest Mentats have a healthy respect for the error factor in their computations," she said.

Finally, remember the worst thing about being a Mentat:

"That's the curse of being a Mentat. You can't stop analyzing your data."